///////////////////////////////////////////////////////////////////////////////////
/// OpenGL Mathematics (glm.g-truc.net)
///
/// Copyright (c) 2005 - 2015 G-Truc Creation (www.g-truc.net)
/// Permission is hereby granted, free of charge, to any person obtaining a copy
/// of this software and associated documentation files (the "Software"), to deal
/// in the Software without restriction, including without limitation the rights
/// to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
/// copies of the Software, and to permit persons to whom the Software is
/// furnished to do so, subject to the following conditions:
/// 
/// The above copyright notice and this permission notice shall be included in
/// all copies or substantial portions of the Software.
/// 
/// Restrictions:
///		By making use of the Software for military purposes, you choose to make
///		a Bunny unhappy.
/// 
/// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
/// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
/// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
/// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
/// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
/// OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
/// THE SOFTWARE.
///
/// @ref gtx_spline
/// @file glm/gtx/spline.inl
/// @date 2007-01-25 / 2011-06-07
/// @author Christophe Riccio
///////////////////////////////////////////////////////////////////////////////////

namespace glm {
    template<typename genType>
    GLM_FUNC_QUALIFIER genType
    catmullRom
    (
            genType
    const & v1,
    genType const &v2,
            genType
    const & v3,
    genType const &v4,
    typename genType::value_type const &s
    ) {
    typename genType::value_type s1 = s;
    typename genType::value_type s2 = pow2(s);
    typename genType::value_type s3 = pow3(s);

    typename genType::value_type f1 = -s3 + typename genType::value_type(2) * s2 - s;
    typename genType::value_type f2 =
            typename genType::value_type(3) * s3 - typename genType::value_type(5) * s2 +
            typename genType::value_type(2);
    typename genType::value_type f3 =
            typename genType::value_type(-3) * s3 + typename genType::value_type(4) * s2 + s;
    typename genType::value_type f4 = s3 - s2;

    return (
    f1 *v1
    +
    f2 *v2
    +
    f3 *v3
    +
    f4 *v4
    ) / typename genType::value_type(2);

}

template<typename genType>
GLM_FUNC_QUALIFIER genType
hermite
(
        genType
const & v1,
genType const &t1,
        genType
const & v2,
genType const &t2,
typename genType::value_type const &s
)
{
typename genType::value_type s1 = s;
typename genType::value_type s2 = pow2(s);
typename genType::value_type s3 = pow3(s);

typename genType::value_type f1 =
        typename genType::value_type(2) * s3 - typename genType::value_type(3) * s2 +
        typename genType::value_type(1);
typename genType::value_type f2 =
        typename genType::value_type(-2) * s3 + typename genType::value_type(3) * s2;
typename genType::value_type f3 = s3 - typename genType::value_type(2) * s2 + s;
typename genType::value_type f4 = s3 - s2;

return
f1 *v1
+
f2 *v2
+
f3 *t1
+
f4 *t2;
}

template<typename genType>
GLM_FUNC_QUALIFIER genType
cubic
(
        genType
const & v1,
genType const &v2,
        genType
const & v3,
genType const &v4,
typename genType::value_type const &s
)
{
return ((
v1 *s
+ v2) * s + v3) * s +
v4;
}
}//namespace glm
